Glass transition behaviour In a voronoi model of cell tissues

Abstract

In this final year project, we characterize the confluent polydisperse Voronoi model in the context of the glass transition. The Voronoi model is useful as a phenomenological approximation to the behaviour of real epithelial cells. Molecular dynamics simulations are carried out with temperature as a varying parameter and the preferred target shape index as a control parameter. This allows one to study the static and dynamical statistical properties in the temperature regime where mode-coupling theory is dominant. Both the dynamic and hexatic correlation lengths are found to have a negative relation with temperature. In contrast, the fragility of the polydisperse Voronoi model is demonstrated to be strong and independent of the preferred target shape index. A strong fragility corresponds to non-increasing potential energy barriers present within Goldstein's energy landscape. Finally, other measures unique only to the Voronoi model are carried out. The area and perimeter auto-correlation functions confirm ergodicity. An unexpected behaviour in the area radial correlation function might justify further investigations.